The Search for Planet Nine

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Friday, September 21, 2018

Greetings! My name is Elizabeth Bailey, and I am a graduate student here at Caltech. As part of my work so far, I have addressed the ongoing search for Planet Nine, in particular the use of mean-motion resonances to infer its present-day location on the sky.

A mean-motion resonance occurs when two bodies orbiting a central body have orbital periods related by an integer ratio. A great example is Pluto and Neptune. Pluto’s orbit is not a perfect circle, but rather a little elongated (e ~ 0.25). It actually crosses Neptune’s orbit, which might lead one to ask if they are on a collision course with each other. Fortunately, the answer is a confident “no.” Neptune and Pluto will never collide, because they are in a 3:2 (pronounced “three-to-two”) mean motion resonance with each other. Meaning, for every three trips Neptune completes around the sun, Pluto completes exactly two. It’s as if they’re dancing with each other. Every three times Neptune steps into the intersection of their orbits, Pluto steps twice somewhere else, and they don’t step on each other.

So what does this have to do with Planet Nine? If Planet Nine exists, the distant KBOs it shepherds may very well experience resonant interactions with it. In fact, this was already pointed out in Konstantin & Mike's original Planet Nine paper, and is at this point relatively well understood. As a result, we can reasonably expect that at least some of the observed KBOs are currently locked into resonances with Planet Nine, and if we can understand the machinery of these interactions, perhaps we can infer the location of P9.

In a sense, the distant solar system is a lot like a giant cosmic nightclub. In this analogy, we are scanning the dance floor for Planet Nine, but it's hanging out in a dark corner somewhere in the back, while everyone is doing a P9-themed dance. So rather than looking for P9 itself, we are instead trying to figure out where it is by studying the KBO mosh-pit. This brings us to the key problem at hand: is this feasible in practice? We address this question in our recent work, published in the Astronomical Journal.

The short answer is no - using resonances does not appear to be a feasible approach to find Planet Nine. Here's a figure from the paper comprised of seven histograms, corresponding to simulations with seven different eccentricities of Planet Nine (e_9 = 0.1, ..., 0.7) showing the count of objects occupying individual resonances. (The 2:1 resonance is located at "2" on the horizontal axis, and the 3:2 resonance is located at "1.5," and so forth.)

The takeaway point from this figure is that although you do find a lot of KBOs at the big-name resonances like 3:2 or 1:1, there are many objects occupying other resonances with larger integers in their names, like 14:5 or 2:7. There is a disturbing consequence of the mathematical nature of the planetary disturbing function (yes, it is actually called "The Disturbing Function" in celestial mechanics literature) which, upsettingly, suggests that these so-called high-order resonances become increasingly important when dealing with eccentric planets like Planet Nine, and the results of computer simulations presented in this work confirm this. In summary, because Planet Nine is eccentric, it carries out very complicated dance moves with the KBOs.

It's worth mentioning that the simulations used to make this figure were simplified in comparison to reality. The canonical giant planets Jupiter through Neptune were treated as a static ring of mass (this is often referred to as the “secular” approximation), and the solar system is treated as a flat 2-dimensional object even though Planet Nine is, in reality, inclined. Think of it as a best-case scenario of sorts: in this physical setup, Planet Nine is the only active perturber of the KBOs. In the real solar system, Neptune is also on the dance floor, behaving in a very disruptive fashion. When KBOs get too close to Neptune, it flings them around. Sometimes those KBOs resume dancing with Planet Nine, but other times they just head out the door into interstellar space.

Suppose, despite these complications, you could determine which individual KBOs are indeed in mean motion resonances with Planet Nine at this time. Then, if this information were to be of any use, you would then need to know the specific resonance of each KBO. In 3-D simulations, there is no obvious concentration of objects at particular resonances (see figure below). Hence, no matter how long we wait for more KBOs to be observed, we have virtually no hope of using resonances to predict Planet Nine's current location along its orbit.

Although based on the results of this work it does not appear feasible to predict the present-day location of Planet Nine along its orbit, this does not by any means imply that Planet Nine is invisible to telescopes. There is still a well-defined swath of sky in which the search for Planet Nine continues. We have merely shown that mean-motion resonances with KBOs are not a useful tool for deciding where point the telescope, so we're back to systematically scanning the sky. Turns out that even in astronomy, the easy way is the hard way.

Monday, May 7, 2018

Hi, everyone! I’m Tali, an undergrad at the University of Michigan. Last summer, I worked on a Planet Nine project with Konstantin and Mike, and although we didn’t find Planet Nine (yet!), we did look further into the stability of objects in the presence of Planet Nine. Turns out, not everything is stable!

In his last post, Konstantin explained that the main cluster of anti-aligned objects is able to remain stable due to mean motion resonances with Planet Nine. Their orbits always cross Planet Nine’s orbit, but such resonances allow the objects to avoid collisions. Here’s an example of what the dynamics looks like: the green orbit is Planet Nine, and pink orbit is an anti-aligned Kuiper belt object. The little blue circle is Neptune’s orbit, and the star is the Sun (not to scale).

What we see here is that the anti-aligned object experiences librations (=bounded oscillations) in the direction its orbit points (the longitude of perihelion). Meanwhile, Planet Nine’s orbit slowly precesses and changes direction as well.

BUT, it turns out that being in resonance with Planet Nine is not enough for stability. That’s because Neptune is still in the picture. Let’s look back at the animation above. Notice that as the pink orbits wags back and forth, its perihelion distance (=the shortest distance from the orbit to the Sun) changes. The pink orbit stretches (and hugs Neptune’s orbit) and then circularizes (and detaches from Neptune). The wider the “wagging the tail” oscillations are, the more pronounced the in and out behavior becomes. If the object librates with too large of an amplitude, it comes suuuuuper close to Neptune. And when that happens, it either gets ejected from the solar system or its dynamics changes entirely, and its behavior is no longer relevant to Planet Nine.

SO, the stability of the anti-aligned objects can be summarized by the two gifs below. When the longitude of perihelion libration (tail-wagging) is mild, our object experiences small changes in perihelion distance, and thus remains at a safe distance from the inner solar system. But, if the librations become too wide (and too wild), the object goes unstable, thanks to Neptune.

STABLE LIBRATIONS

UNSTABLE BEHAVIOUR

Now, the anti-aligned population is not the only one we looked at. Planet Nine carves out an aligned cluster of objects as well, which experience librations in longitude of perihelion, but this time, inside the orbit of Planet Nine:

As you can see this object is in the perfect stable location - it stays far away from Neptune (blue) AND doesn’t cross Planet Nine’s orbit, and just quietly librates in longitude of perihelion. This object is all set for life. Nothing will make it budge from this configuration.

BUT, there are objects that seem to be aligned at first, but suffer because their libration amplitudes are too large. Here’s an example of such an object:

In the animation above, the orbit spins too far and crosses Planet Nine’s orbit. This is not good for two reasons: (i) Planet Nine starts having collisions with this object and knocking it about, and, (ii) UNLESS the object is in a resonance with Planet Nine, it gets swept by Planet Nine into the Neptune scattering region. If you look at the animation carefully after the pink orbit crosses the green orbit, you’ll see that the perihelion distance of the object is slowwwly decreasing. When it gets small enough - when the object starts interacting strongly with Neptune - we get the same output as for the unstable anti-aligned objects (i.e. instability and a crazy jumping dog.)

So, what’s the bottom line? Not all anti-aligned objects are stable! And not all aligned objects are stable. And it all depends on their perihelion distance, which is closely tied with their librations in longitude of perihelion.

Moreover, it turns out that what kind of objects we find surviving through the end of our simulations depends on the initial conditions we put in. What do I mean by initial conditions? Well, for example, we expect that different scenarios of Planet Nine’s formation would have affected the initial configuration of the Kuiper belt in different ways. So, suppose we start with two different initial conditions: a “narrow” Kuiper belt (objects initially within a narrow interval of perihelion distances) and a more widely spread “broad” Kuiper belt. And now we integrate these populations forward, in the presence of Planet Nine, in two separate simulations. Do these populations end up creating the same Kuiper belt?

In our recently accepted paper, we find that they don’t! In fact, the stable aligned population discussed above is completely missing from the “narrow” Kuiper belt. So, as the astronomy community continues to find more and more of these distant Kuiper belt objects, we might be able to start to tell which initial Kuiper belt we started with, and maybe how Planet Nine formed…

Tuesday, October 10, 2017

Every die-hard fan of the scientific method knows that Karl Popper was a baller. While his achievements clearly extend far beyond analysis of the scientific method alone, he is arguably best known for his work on empirical falsification. In essence, the idea behind his argument is that a theory is only any good if there exists a direct and clear experimental/observational way to demonstrate that it is incorrect. In other words, it is more important to point out avenues in which your theory can be wrong than to flaunt all the possible ways it could be right.

Why am I writing about this? Mike and I just spent a week at 14,000ft on the Big Island directly searching for Planet Nine, and I’ve been thinking a lot about how Popper’s falsifiability criteria apply to the Planet Nine hypothesis… Obviously, if we search the entire sky at sufficient depth and don’t find Planet Nine, then we are plainly wrong. But I don’t think this is going to happen. Instead, I think we (or some other group) are going to detect Planet Nine on a timescale considerably shorter than a decade - maybe even this year if we/they get lucky. Which begs the question: if a planet beyond Neptune is found, how would we proceed to determine that the Planet Nine theory is actually right?

Figure 1. Mike and I at the telescope - where colors don't exist.

I’m sure this question sounds incredibly stupid, so let me back up a bit. The Batygin & Brown 2016 AJ paper is by no means the first to predict a trans-Neptunian planet with a semi-major axis of a few hundred astronomical units. That accolade goes to George Forbes, who in 1880 proposed a planet located at ~300AU, based upon an analysis of the clustering of the aphelion distances of periodic comets (sound familiar?). Since then, a trans-Neptunian planet has been re-proposed over and over again, which brings us to problem at hand: whose trans-Neptunian planet theory is right and whose is wrong?

In my view, there is a very clear and intelligible way to answer this question. Each proposition of a trans-Neptunian planet is uniquely defined by (i) the data it aims to explain and (ii) the dynamical mechanism that sculpts the observations. So in order to be deemed correct, the discovered planet must match both of these specifications of the theorized planet.

Figure 2. The current observational census of distant KBOs.

When it comes to the Planet Nine hypothesis, point (i) is well-established: Planet Nine is invoked to explain (1) physical clustering of distant Kuiper belt orbits, (2) the perihelion detachment of long-period KBOs such as Sedna and VP113, as well as (3) the origin of nearly-perpendicular orbits of centaurs in the solar system. Embarrassingly, until recently our understanding of the “machinery” behind how Planet Nine generates these observational signatures has been incomplete. That is, although we have plenty of numerical experiments to demonstrate that Planet Nine can nicely reproduce the observed solar system, the theory that underlies these simulations has remained largely elusive.

The good news is that this is no longer a problem. In a recently accepted paper that I co-authored with Alessandro “Morby” Morbidelli, the theory of Planet Nine is characterized from semi-analytical grounds. So, for the first time, we not only know what Planet Nine does to the distant Kuiper belt, but we understand how it does it.

The first lingering question that Morby and I tackled is that of stability: how do the distant Kuiper belt objects avoid being thrown out of the solar system by close encounters with Planet Nine, when their orbits intersect? Turns out, the answer lies in an orbital clockwork mechanism known as mean motion resonance (MMR). When a Kuiper belt object is locked into an MMR with Planet Nine, it completes an integer number of orbits per (some other) integer number of orbits of Planet Nine. This strict rationality of the orbital periods allows the bodies to exchange orbital energy in a coherent fashion, and ultimately avoid collisions.

But how do such configurations arise in nature? Remarkably, the answer in this case is “by chance.” When the Kuiper belt first formed, a staggering number (roughly 30 Earth masses worth) of small, icy asteroid-like bodies were thrown out into the distant realm of the solar system by Neptune (for the interested reader, see papers about the Nice model here and here). Most of these objects were not fortunate enough to accidentally land into mean motion resonances with Planet Nine and were ejected from the solar system. However, the few that were, survive in the distant Kuiper belt to this day, and comprise the anti-aligned cluster of orbits that we observe. As a demonstration of this point, check out the simulated orbital period distribution of surviving Kuiper belt objects in one of our idealized simulations, and note that all distant bodies have rational orbital periods with that of Planet Nine:

All of this said, the full picture is of course not as clear-cut. Within the context of our most realistic calculations of distant Kuiper belt evolution, the clustered KBOs chaotically hop between resonances, instead of staying put. Still, the qualitative framework provided by analysis of isolated resonances holds well, even in our most computationally expensive simulations.

Ok so this resolves the question of how Kuiper belt objects survive, but it leaves open the question of why their orbits are clustered together. Intriguingly, a qualitatively different dynamical mechanism - known as secular interactions (see here for a neat discussion) - is responsible for the orbital confinement that we see. Plainly speaking, over exceedingly long periods of time (e.g. hundreds of orbits), Planet Nine and the Kuiper belt objects it perturbs will see each-other in almost every possible configuration along their respective orbits. Thus, their long-term evolution behaves as if the mass of Planet Nine has been smeared over its orbital trajectory, and its gravitational field torques the elliptical orbit of the test particle. The plot below shows the eccentricity-longitude of perihelion portrait of this secular dynamic inside the 3:2 mean motion resonance, where the background color scale and contours have been computed analytically and the orange curve represents a trajectory drawn from a numerical simulation.

Indeed, the fact that the semi-analytic theory predicts looped trajectories that cluster around a P9 longitude of perihelion offset of 180 degrees implies that the raising of perihelion distances (i.e. lowering of eccentricities) of long-period KBOs and anti-aligned orbital confinement are actually the same dynamical effect. In other words, the reason that objects such as Sedna and VP113 have orbits that are not attached to Neptune is because they are entrained in the peculiar anti-aligned secular dynamic with Planet Nine.

Finally, there is the puzzle of the highly inclined orbits. Whenever one sees cycling of orbital inclination and eccentricity, there is a temptation to invoke the Kozai-Lidov mechanism as the answer. In the case of Planet Nine, however, the high-inclination dynamics are keenly distinct from those facilitated by the Kozai-Lidov effect. Perhaps the most obvious reason why the dynamics we observe in numerical simulations is not the Kozai-Lidov effect is that in our calculations, highly inclined KBOs develop the highest eccentricities when their orbits are perpendicular to the plane of Planet Nine’s orbit, in direct contrast with perpendicular and circular orbits entailed by the Kozai-Lidov effect.

So if it’s not the Kozai-Lidov resonance, then what is it? As it turns out, the high-inclination dynamics induced by Planet Nine is characterized by the bounded oscillation of a octupole-order secular angle which is equal to the difference between the longitude of perihelion of the KBO relative to that of Planet Nine and twice the KBO argument of perihelion. How could we have ever thought it was anything else?… The plot below shows the high-inclination secular resonant trajectories executed by test-particles in our simulation plotted in canonical action-angle coordinates, with the observed objects shown in orange. Examining this plot closely, one detail that I’m reminded of is the fact that the few high-inclination large semi-major axis centaurs that we know of are actually the “freaks” of the overall population, since they all have perihelia on the order of ~10AU. Certainly, detecting a sample of these objects with perihelia well beyond 30AU would be immensely useful to further constraining the parameters of the model.

With the above rambling in mind, I will admit that all I’ve mentioned here is an introductory account of the paper. As such, it represents a considerable simplification of our actual calculations, so if you want to better understand the full picture, I can only urge you to read the paper itself. Importantly, however, the work presented in this manuscript not only provides us with a better understanding of how the observed census of distant KBOs has been sculpted by Planet Nine, it finally places the P9 hypothesis within the framework of Popper’s demand for falsifiability, and sincerely allows for the confrontation of the Planet Nine theory with the observational search. The final step is now to find it.

Thursday, September 21, 2017

We haven’t found Planet Nine yet, in case you were
wondering. To date, the telescopic searches have really just begun to scratch the
surface of the area that needs to be scanned, and, while clever new projects to
find Planet Nine with different techniques have been proposed, most of these
efforts are just getting underway. But don’t worry: the new season of Subaru searching starts tonight! With
good weather, we should be able to scan a significant part of our search
area. Stay tuned.

To get ready for this new season of searching for Planet Nine, we have spent most of the last year developing our understanding of the way that Planet Nine interacts with the rest of the solar system. Much of this has involved large amounts of analytic and computational work to figure out what the orbit
of Planet Nine looks like and where in its orbit Planet Nine is. If we could
figure that out perfectly, we could simply go out tonight and point our
telescopes right at it, as was done for the discovery of Neptune in 1846.
Sadly, we have less information on Planet Nine than Le Verrier did for Neptune
in 1846, so we’re not able to pinpoint it just yet, but we are able to
constrain what the orbit looks like and, thus, where we should look.

I suspect that most people don’t really care to know the
details of how we’re trying to figure out where Planet Nine is. But one group
cares a lot: the other astronomers actively looking for Planet Nine. Since our
first prediction of the existence of Planet Nine, we’ve tried hard to keep
anyone who wanted to know up to date on where we think the best places to
search are. The more people who are involved in looking in the more different
ways, the more quickly Planet Nine will be detected, so part of our work of
trying to figure out the orbit of Planet Nine is for the sake of all of these
other groups.

To understand where we think Planet Nine might be right now,
we need a long digression on orbits (if you’re intimately familiar with
Keplerian orbital elements or simply don’t want to know, please skip ahead!).
All objects in the solar system travel on elliptical paths around the sun, with
the sun at one of the foci of the ellipse. If you’re on the Earth looking at the
sky, however, the path of the orbit doesn’t look like an ellipse, it simply
looks like a great circle across the sky with you at the center (on Earth, a
great circle is like a line of longitude, or like the equator; lines of
latitude that are not the equator are not great circles; it works the same in
the sky). If I want to describe the orbital path
of Planet Nine, then, I need to tell you where this great circle is. To describe
any great circle, you only need to know two numbers. There are many different
ways to define these two numbers, but we will use (1) the longitude where the
great circle crosses the equator (which on the sky we just define to be the
extension of the Earth’s equator) when it crosses from south to north (all
great circles cross the equator twice 180 degrees apart, so we had best specify
which of the two we mean), and (2) the angle that the orbit makes with respect
to the equator when it crosses the equator. In celestial mechanics, these two
numbers are called the longitude of the ascending node (ascending =
south-to-north; get it?) and the inclination. If we knew these two numbers
perfectly we would know the exact path that Planet Nine takes across the sky. (The
motion of the Earth complicates things a little, but because Planet Nine is so
far away we can mostly ignore those details.) If we wanted to point a telescope
directly at Planet Nine, all we would need to know are the longitude of ascending node (which I’ll just call “node” from now
own), the inclination, and (3) where
within the orbit the planet is. We’ll call this last parameter the orbital longitude and simply define it
as the longitude in the sky where the object is (this definition is not the norm
of celestial mechanics, where instead you’ll get mean anomaly or eccentric
anomaly or other more complicated things; we’ll stick with this easier to
understand version).

While the first three parameters tell the path across the
sky and where the object is, they don’t tell you anything about the shape of
the orbit or how far away the planet is (which we care about because that helps
us estimate how bright it should be and whether or not it should have already
been spotted in parts of its orbit). We know that Planet Nine goes in an
ellipse around the sun. The shape of the ellipse is completely specified by (4)
knowing the average distance of the object from the sun and by (5) a number
from 0 to 1 which defines how elongated the object is (zero means it is a
circle, 1 means it is so elongated that it never closes back in on itself). We
call these semimajor axis and eccentricity.

You need one last number. While we now know the shape of the
orbit and the orbital plane, we are still don’t know how the orbit is oriented
within its plane. We can specify that by (6) determining the longitude when the
orbit comes the closest to the sun. We call this last parameter the longitude of perihelion (this is a bit
of a simplification, but an unimportant one). The figure below illustrates what
it means to keep (1)-(5) fixed and only change the longitude of perihelion. The
shape and orbital plane of the planet are fixed, and we are simply spinning the
orbit around on its axis.

(If you skipped the details about Keplerian orbital elements,
come back now!)

Those are a lot of things to learn if we want to find Planet
Nine. Here’s how we’re making progress.

The easiest orbital parameter for us to extract is the
longitude of perihelion of Planet Nine. Why? Because the main observable effect
of Planet Nine is to capture distant eccentric Kuiper belt objects into orbits
which are what we call anti-aligned with Planet Nine (see the illustration at
the top of the page!). “Anti-aligned” means, precisely, that the longitude of
perihelion of the Kuiper belt objects is (on average) 180 degrees away from
that of Planet Nine. We now know of about 10 of these anti-aligned objects, so
can look at their longitudes of perihelion and get a direct estimate of the
longitude of perihelion of Planet Nine (if you care about the details: we
actually excludethe two most recently
detected objects as they came from the OSSOS survey which has been shown to
have striking biases in the objects that it finds). When we do this, we find a
value of 235 with an uncertainty of 12 degrees. This is a great start, but we
have 5 more parameters to go (and longitude of perihelion doesn’t actual help
tell us the orbital path through the sky).

In our second paper about a year ago, we used a suite of
computer simulations to see how Planet Nine would affect eccentric objects in
the Kuiper belt if we varied all of the other parameters. We found some key
results. If Planet Nine comes too close it tears up the Kuiper belt. If it
stays too far away it does too little. If Planet Nine is too inclined it has
only a small effect. Those constraints help on everything except for the node
of Planet Nine and the actual longitude of Planet Nine. Without the node,
though, we really have no constraint on the orbital path at all! We made some
estimates by using a different quantity, but those estimates were the least satisfying
part of the analysis. Nonetheless, those led to our best estimates of where to
look, and the picture that you have all seen here.

Since that last paper, though, we have learned a lot more
about the physics of how the gravity of Planet Nine affects the orbits of
distant objects in the Kuiper belt. Luckily, one of the things we now
understand much better is how to constrain the node of Planet Nine.Early on, we recognized that all of the
distant eccentric Kuiper belt objects had similar longitudes of ascending node,
and it seemed clear that these must be related to that of Planet Nine somehow.
With some even more realistic follow-on computer simulations we realized that
what we had surmised was right: the distant eccentric Kuiper belt objects have
the same average node as Planet Nine. Planet Nine partially pulls these distant
objects into its own orbital plane. But only partially. The distant objects, on
average, do not have the same inclination as Planet Nine. The distant objects
live in an average orbital plane that is close to midway between that of the 8
other planets and Planet Nine. Though this result is simple to state, a lot of
work (or perhaps a lot of electricity for computers) went in to that statement!
And the good news is that can now estimate the node much more precisely. If we
take those same eccentric distant Kuiper belt objects and look at their nodes,
we find that Planet Nine has a longitude of ascending node of ~94 degrees. The
average inclination of those objects, by the way, is 18 degrees, so we know
that the inclination of Planet Nine is higher than this, but not much higher,
because otherwise, as we found earlier, it doesn’t make an anti-aligned
population.

I know, I know, saying that we now know the longitude of
ascending node of Planet Nine does not sound exciting to most people. But we
have reduced the uncertainty on this parameter by a factor of 5, which is
essentially as good as having done a search of 80% of the relevant sky! OK.
Sort of.

Now, if you’ve been paying close attention, you know what I
want to know next. We only have general constraints on the inclination of
Planet Nine, and we have no real constraints on the longitude. How are we going
to find those? I think the solution is doing the same sorts of computer
simulations but sort of in reverse. We have been doing new computer simulations
where we take the ~20 known objects whose orbits are thought to be affected by
Planet Nine and we have put them into their current positions in the solar
system today. We then put a Planet Nine in and watch what happens. Sometimes
the simulated Planet Nine sends everything flying. Sometimes after a billion
years the solar system looks close to the same as it does today. We learn
general things: large inclinations are bad, having Planet Nine too far away
doesn’t make a powerful enough effect. How exactly to balance these constraints
is not yet obvious, but through about a 100 trillion cumulative years of
simulating the real objects in the outer solar system I think we’re getting
close.

In my perfect fantasy world these latest simulations will
tell us more or less where Planet Nine is and we will simply go look and it
will be there as Neptune was. Probably that is asking too much of reality. But
we’re going to give it a try. In the mean time, we are slowly narrowing down the region of the sky in which we need to search. If you're looking for Planet Nine, go look there!

Sunday, July 2, 2017

I ended the last post by pointing out that the Planet Nine hypothesis, as currently formulated, entails a theoretical solution to five seemingly-unrelated observational puzzles: (i) orbital clustering of a>250AU KBOs, (ii) dynamical detachment of KBO perihelia from Neptune, (iii) generation of perpendicular large-semi-major axis centaurs, (iv) the six-degree obliquity of the sun, and (v) pollution of the more proximate Kuiper belt by retrograde orbits. Virtually all of the discussion surrounding the new OSSOS dataset to date has focused on long-period orbits and the statistical significance of perihelion clustering beyond ~250AU - a concern relevant exclusively to point (i). Breaking with this trend, in this post I want to examine a shorter-period component of the new data, and discuss how it relates to arguably the most unexpected consequence of P9-driven evolution: generation of retrograde orbits with semi-major axes smaller than ~100AU (i.e. aforementioned point (v)).

Those of you who have been following the P9 saga for more than a year might remember the article by Chen et al. from last August, which reported the detection of Niku, a ‘rebellious’ Kuiper belt object that orbits the sun in the retrograde direction (see news coverage here and here). While the orbit of Niku itself is in some sense unremarkable (because it is acutely similar to the orbit of Drac - another retrograde object that was detected back in 2008), this discovery did successfully reinvigorate the community’s interest in the high-inclination population of the trans-Neptunian region.

Here is a look at all objects within the current dataset with inclinations greater than 60 degrees, semi-major axes in the range of 30AU to 100AU, and perihelion distance in excess of Jupiter’s orbit:

For scale, Neptune’s orbit is shown here as a blue circle, and the orbits of Niku and Drac are emphasized in gray. Generally speaking, these bodies trace out an apparently-random orbital structure and raise an important question regarding the physics of their origins, since none of them can be reproduced by conventional simulations of the solar system’s early evolution.

Unlike objects such as Sedna and 2012 VP113, Niku and Drac are currently quite close to Neptune itself, and have semi-major axes that are much too small to interact with Planet Nine directly. Nevertheless, in a paper published last October, we showed that Planet Nine naturally leads to their production. The crux of our result is that the current orbits of these bodies are very different from their primordial ones. Specifically, in our simulations we noticed that Kozai-Lidov type oscillations experienced by distant Kuiper belt objects due to Planet Nine can drive them onto highly inclined, Neptune crossing orbits. Subsequently, close encounters with Neptune shrink the orbit, freezing it onto a retrograde state. Mark Subbarao from Adler Planetarium has kindly created this visualization of one of our simulated particles, that ends up on an orbit that is almost an exact replica of Niku and Drag (grab the video here if the player below does not work):

In addition to the observed objects that were already known back in October of last year, this plot shows two new data points that also fit the simulated pattern beautifully. Thus, the predictions of the Planet Nine hypothesis have held up very well within the more proximate part of the trans-Neptunian region, where the planet’s direct influence is minimal.

So where does the new data leave us? Let’s summarize: while the membership of the primary perihelion cluster has gone from six to ten, the distant belt now also has some objects that do not belong to the apsidally anti-aligned population of long-period KBOs. Despite worries of Planet Nine’s immediate demise, it is pretty clear that these bodies fit well with other dynamical classes predicted by the model, so there’s no real conflict there. Closer to Neptune, we’ve picked up a couple high-inclination objects that also agree well with the model. Sigh…

Cumulatively, I can’t help but feel an uneasy combination of relief and disappointment. On one hand, the agreement between simulations and data implies that the theoretical model remains on solid footing. As we head into upcoming P9 observing season, this is important and reassuring. On the other hand, we haven’t learned anything genuinely new from the expanded dataset, and P9’s precise location on its orbit as well as a well-founded qualitative description of P9-induced dynamics remain somewhat elusive. Clearly, much work - both theoretical and observational - remains to be done. So back to research.

Friday, June 30, 2017

It has been an exciting and turbulent couple of weeks in Planet Nine land. The OSSOS survey has released their full data set, which in addition to over 800 garden-variety Kuiper belt objects, contains four little worlds with semi-major axes beyond 250AU. Together with the previously published data, this brings the count of distant bodies relevant to the P9 hypothesis up to 13 - a whopping 117% increase in the census of long-period KBOs, compared with what we had back in early 2016.

When viewed from above, the orbits of the objects look like this:

So what story does the newly updated data foretell? Let’s look at the dry facts first. The membership of the primary orbital cluster that we pointed out in the first paper (shown in purple) has grown to ten. Meanwhile, two of the objects (shown in green) have orbits that are diametrically opposed to the primary cluster. Finally, there is also a single outlier, 2015 GT50, shown in gray. Cumulatively, this is a somewhat more complex picture than what we had a couple years ago.

If you look at the OSSOS data in isolation, it contains two objects that are in the purple camp, one green orbit, and the gray outlier. You need to know exactly zero statistics to conclude that these four points DO NOT form a pattern. And this is what the OSSOS team concludes as well, after carrying out a sophisticated account for the observational biases inherent to their survey. Indeed, from the independent OSSOS dataset alone, a random underlying distribution (as opposed to a clustered distribution) cannot be ruled out.

When you look at the full dataset, however, the propensity for orbital clustering is clear. Shankman et al. argue that this clustering is unlikely to be real, and is merely apparent. That is, in their view, observational biases conspire to make certain parts of the night sky more observable than others, leading to the discovery of orbits that share a common orientation more frequent. In striking contrast, a recent paper that Mike put together shows exactly the opposite to be true for the non-OSSOS dataset: observational bias cannot account for orbital clustering beyond 250AU.

Perhaps the resolution lies in that observational surveys that discovered non-OSSOS objects share very little in their design with OSSOS, leading to staggeringly different biases between the OSSOS and non-OSSOS datasets. But one way or another, the likely take away message here is that although the data shows a statistically significant tendency for clustering, the emergent story is not as simple as that of all orbits with periods longer than ~4000 years (or equivalently, semi-major axes greater than 250AU) sharing a common orientation. Rather, the primary orbital cluster is accompanied by a diametrically opposed population of orbits, and is contaminated by an outlier.

Let’s now compare this picture with theory. Numerical simulations of solar system dynamics that include P9 (e.g. BB16aBB16b) predict that beyond semi-major axis of 250AU, there will be a strong, long-term stable cluster of bodies with orbits that are anti-aligned with respect to the major axis of P9 as well as a weaker, metastable cluster of objects that are aligned with the orbit of P9. From an evolutionary point of view, objects belonging to the anti-aligned cluster are those that were scattered into distant orbits billions of years ago and were locked into an immutable, resonant pattern of anti-aligned perihelion libration. On the other hand, aligned orbits are those that were scattered out by Neptune (from a lower semi-major axis region) comparatively recently (e.g., ~ hundreds of millions of years ago), and due to mean-field interactions with Planet Nine will be ejected from the solar system as soon as their orbits precess out of alignment with that of P9.

Within the context of this theoretical expectation, the purple and green orbits depicted in the above picture are readily interpreted as members of the anti-aligned and aligned clusters respectively. To this end, here is a plot of orbital orientation (longitude of perihelion relative to the major axis of Planet Nine) vs. particle semi-major axis where the data are color-coded in the same way as in the above graphic, while blue and orange points show dynamical footprints of the long-term stable and metastable simulated particles respectively:

If we adopt this interpretation, the purple data points are drawn from the distribution of simulated objects shown in blue, while the green points belong to the orange population of test-particles. Although this explanation is comforting, we pretty much knew this already. So there is nothing particularly surprising here.

The data point I got considerably more intrigued by is the outlier, 2015 GT50. As already mentioned previously, this object does not belong to either the aligned or anti-aligned cluster, so naively speaking it simply doesn't fit the model. A more cursory inspection of the above plot however, brings to light the existence of a string of specific orbital radii that correspond to resonances with Planet Nine, where the simulated objects circulate through the full 0-360 degree range of orbital orientations. Remarkably, the outlier (2015 GT50) falls *exactly* on one such orbit (i.e. note on the plot above that the gray point falls on a vertical blue line).

This is kind of staggering. Without changing the Planet Nine parameters at all (to make this plot I’ve adopted the same a=700AU e=0.6 m=10Mearth P9 configuration as in the original Batygin & Brown 2016 AJ paper), the model manages to fit all the data, including the supposed outlier. Of course, the fact that the observed object fits so well with theory might be a coincidence, but this correspondence nevertheless emphasizes that the mere existence of a small number of apsidally unconfined objects that do follow the overall pattern exhibited by the data, does not constitute strong evidence against the Planet Nine hypothesis. Instead, mapping out this comparatively uncommon population of unconfined objects might lend important constraints on P9’s semi-major axis.

There is one other crucial aspect here, which is that the clustering of a>250AU orbits constitutes only one line of evidence for Planet Nine. If that were the entire story, the P9 hypothesis would have never made it to publication, because we would not have submitted the paper. Instead, what makes the theoretical case for Planet Nine compelling is its capacity to simultaneously explain (i) orbital clustering, (ii) dynamical detachment of KBO perihelia from Neptune, (iii) generation of perpendicular large-semi-major axis centaurs, (iv) the six-degree obliquity of the sun, as well as (v) pollution of the more proximate Kuiper belt by retrograde orbits. In my view, it is only when these pieces of the puzzle are put together that Occam’s razor begins to cut in Planet Nine’s favor. But in the end, time will tell - unlike many theoretical questions, the existence of Planet Nine has a well-defined observational resolution, and we’ll know the answer in less than a decade.

Thursday, May 4, 2017

Last year, just after Konstantin and I announced our hypothesis that a
distant massive planet in an eccentric orbit was corralling distant
Kuiper belt objects into peculiar orbits, I wrote a post explaining why
it might all be wrong. Not that it I thought was all wrong – I was and
still am quite convinced that Planet Nine is out there waiting to be
found – but it’s always good to understand how a hypothesis might be
wrong, particularly when it’s one of your own.

The biggest worry with the original evidence for Planet Nine was that we
might have stared at our own data for so long that patterns were
appearing out of the randomness. This sort of pattern finding is what
leads to people discovering faces on Mars or deities in burnt toast or,
sometimes, giant planets in the void of space. As you remember, the
evidence for the existence of Planet Nine was that the six most distant
know objects in the Kuiper belt were all swept off in one direction and
also systematically tilted in the same direction (see the top of this
page!), contrary to how they should be. We calculated a probability that
such an alignment should occur due to chance, and we came up with
something like one-in-a-million. This calculation is one place our
hypothesis could go wrong. Though I think we did this calculation in a
sensible way, these sorts of after-the-fact calculations should always
be looked at a little suspiciously. A much better approach is to use
your hypothesis to predict what will happen in new data. We did exactly
this when we predicted the presence of objects with orbits perpendicular
to the solar system and then realized these objects indeed existed. For
Konstantin and I this prediction was what changed Planet Nine from
being a cute idea to a solid and viable hypothesis. Even that successful
prediction, however, was less central to the main observation of an
aligned set of distant objects. What I really wanted to see was whether
or not future discoveries would live up to our specific predictions.

It’s been a year now. How has the hypothesis fared?

First, let’s review the specific predictions.

(1) Newly discovered distant Kuiper belt objects (specifically those
with semimajor axis beyond 230 AU, for the sticklers out there) will
continue to have orbits the sweep off in the opposite direction of the
hypothesized orbit of Planet Nine

(2) These objects will be systematically tilted the same way as the original 6 objects.

Our second paper, a few months later, made a third prediction:

(3) In addition to all of the distant objects swept in the opposite
direction, there should be a small population of distant objects with
orbits in the same direction as Planet Nine. No such objects were known
but they must also exist in the Planet Nine hypothesis is true.

Finally, in a talk at a scientific conference in October, after some
even more detailed computer simulations, we made one last prediction, or
perhaps we should call it a modification of the second prediction:

(4) Newly discovered objects will have orbital planes that are, on
average, tilted in the same direction, but there will be a systematic
spread in that tilt.

This last prediction is difficult to explain but easy to show. Every
object orbiting the sun has an orbital north pole. Objects which are
tilted exactly the same will all have the same north pole. We can
represent the tilt of the orbit of an object by the position of its
north pole on a top-down view of its latitude and longitude. In this
plot, the degree of the tilt of the orbit of the object is the distance
from the center of the plot, which the direct of the tilt of the orbit
of the object is the direction from center to the point. Any objects in
the exact orbit plane of the solar system will have a pole latitude of
90 degrees, and will plot right in the center of the plot. Our latest
round of computer simulations showed us to expect a cluster of pole
positions all tilted off in one direction, but with a larger spread than
we had anticipated in prediction (2). The comparison of the computer
simulations of the expected pole positions with the real pole positions
of the six distant objects was good, but that’s not surprising, as we
designed the computer simulations to match the known objects. The
question will be: where do future discoveries lie? Note that it is
pretty easy for any one object to satisfy this prediction, as the
predicted pole positions cover a pretty wide swatch of the sky, but in
general they cluster more strongly off in one direction.

Poles of distant
Kuiper belt objects. The original six objects all had poles tilted
approximately in the same direction, as can be seen by the red points.
The small black dots show the poles found in computer simulations. While
they concentrate near where the red dots are, they cover a much wider
range of space.

Since then we’ve been waiting to see what might be discovered. It’s slow
going. From 2000 until 2013 only six distant objects had been found.
Happily, astronomers have been busy, and 4 new distant objects have been
announced just in the past nine months. Where are they? Let’s take a
look.

The most interesting set of objects came from Scott Sheppard and Chad
Trujillo – the same group that realized early on that something fishy
was going on in the outer solar system and that inspired us to try to
figure it out. Sheppard and Trujillo found 3 distant objects. Two of
them fit right into the pattern of the previous 6 objects. They are both
swept off in the correct direction, and their orbital poles fit within
the range of our computer simulations (again, though, this is a large
range to fit into. Sorry. Blame Planet Nine). The third new distant
object, though, is my favorite. It is swept into an orbit exactly
opposite of all of the rest. This object was precisely the type
predicted for the new population we had predicted, and it was in exactly
the right spot. How exciting was it to see this newly predicted
population? Let’s just say I did a little dance in my office when I saw
the orbit.

The orbits of the
most distant Kuiper belt objects. The red objects are the original six,
the green are the Sheppard & Trujillo discoveries, while the blue
is the OSSOS discovery.

Most recently, the OSSOS team announced the discovery of a single
distant object. If you look where its orbit lies and then you look at
its pole, you will not be surprised to learn that the announcement of
this discovery again had me doing a little dance in my office. Four for
four! But then you might also be surprised that the astronomers making
the announcement claimed that it showed that there was probably no
Planet Nine, partially based on the fact that the pole is not tilted
enough. What? Ah, it’s because they’re looking at the rather simple
prediction (2) and not taking into account the refined understanding
that led to prediction (4). That’s OK. The discussion of prediction (4)
took place at a scientific conference, and the paper describing it,
though submitted for publication, has not yet come out. It’s always
hard for scientific authors to know how to acknowledge these sorts of
things, and so, though the authors knew about the prediction, they
hadn’t had the opportunity to read a detailed paper describing it, so
they chose to not mention it. We’ll still count it.

We now have a score card! Originally there were six objects. Now there
are ten. That’s a 66% increase, which is good work, mostly thanks to
Sheppard & Trujillo’s efforts. And every single discovery fits a
true prediction perfectly. By “true prediction” I mean an authentic
prediction about something not yet seen, rather than an after-the-fact
explanation. Those are hard. Those are the things that we give serious
credence to, as a fun idea turns into a compelling hypothesis turns into
a rigorous theory.

Are we there yet? No. I would put us about halfway between compelling
hypothesis and rigorous theory. There are still a few details about
Planet Nine and its effect on the outer solar system that we can’t yet
explain. But we’re close. When (or, to be fair, I should say “if”) those
details are nailed down, I will be happy to put Planet Nine into the
category of rigorous theory. Of course, we might get lucky and actually
find it first. Then it will simply be confirmed fact.

The season for hunting Planet Nine is coming upon us soon (we predict
that Planet Nine will most likely be discovered near the constellation
Taurus, which starts to rise in the fall). With all of these new
discoveries and, significantly, with our improved understanding of the
way in which Planet Nine gravitationally effects the objects of the
outer solar system, it’s time to update our predicted positions for all
of those searching for Planet Nine. The next two posts will be a bit
technical, but will give the most detailed information for anyone out
there trying hard to find Planet Nine. Good luck, and, um, tell me if
you find it.